Driving assistance method for a vehicle, control unit, driving assistance system, and vehicle

ABSTRACT

A driving assistance method for a vehicle. An instantaneous speed of the vehicle and an instantaneous yaw rate of the vehicle are ascertained. An operation of self-locating of the vehicle is carried out on the basis of the ascertained, instantaneous speed and the ascertained, instantaneous yaw rate of the vehicle. To that end, an instantaneous circumferential wheel speed of one or more wheels of the vehicle is directly measured, evaluated and taken as a basis of the determination of the instantaneous speed and the instantaneous yaw rate of the vehicle.

FIELD

The present invention relates to a driving assistance method for avehicle, a control unit for a driving assistance system of a vehicle,and a driving assistance system, as well as a vehicle, as such.

BACKGROUND INFORMATION

Driving assistance methods and systems for vehicles enjoy increasingpopularity. An important aspect of such methods and systems is theability of the vehicle to self-locate, for example, with regard topositioning and orientation of the vehicle with respect to a roadway,surrounding objects, the surrounding traffic, and, in particular, withrespect to a parking space or the like.

In conventional systems and methods, signals of so-called wheel impulsecounters (WIC's) are used due to the real-time demands of such drivingassistance methods and systems. However, in the low-speed range, forexample, while parking at less than 5 km/h, these supplied values oftenhave insufficient measuring accuracy.

SUMMARY

A driving assistance method in accordance with an example embodiment ofthe present invention may have the advantage that measured values havingsufficient measurement accuracy for the self-locating of a base vehicleare also supplied in the low-speed range. According to an exampleembodiment of the present invention, this is achieved by in that adriving assistance method for a vehicle is provided, where (i) aninstantaneous speed of the vehicle and an instantaneous yaw rate of thevehicle are ascertained; and where (ii) an operation of self-locating ofthe vehicle is carried out on the basis of the ascertained instantaneousspeed and the ascertained instantaneous yaw rate of the vehicle; to thatend, an instantaneous circumferential wheel speed of one or more wheelsof the vehicle being directly measured, evaluated and taken as a basisof the determination of the instantaneous speed and the instantaneousyaw rate of the vehicle. The measurement of the circumferential wheelspeed of one or more wheels may be accomplished at a higher measurementaccuracy than the measured values of wheel impulse counters normallyused. Due to this, the present invention also produces, all in all, ahigher accuracy in the case of the self-locating of the base vehicle.

Preferred further refinements of the present invention are describedherein.

In one preferred specific embodiment of the driving assistance method ofthe present invention, a specific, instantaneous circumferential wheelspeed is measured and supplied by a circumferential wheel speed sensor.

It is particularly advantageous if, in a specific embodiment of thedriving assistance method of the present invention, a time delay of ameasured, instantaneous circumferential wheel speed is compensated forby temporally extrapolating measured values at an earlier measuring timeto a current evaluation time. Using this measure, the relevance to thepresent of, or the presence of, the measurement data, which is notalways adequate in the case of many circumferential wheel speed sensors,due to a time delay, may be compensated for, which means that advantagesof a real-time application preferably ensue.

A particularly simple embodiment of the compensation may be arrived at,if it is implemented (i) by integrating with respect to time, from theearlier measuring time to the current evaluation time, (ii) on the basisof one or more measured values regarding an instantaneous accelerationof the vehicle and/or on the basis of a single-track model of thevehicle.

In another advantageous exemplary embodiment of the driving assistancemethod according to the present invention, a particularly advantageousand rapid capability of executing the individual processing steps isyielded, if, during the determination of the instantaneous speed and theinstantaneous yaw rate of the vehicle, an operation of Moorepseudoinversion is made available and applied to the ascertainedcircumferential wheel speeds. Through these intended measures, arelationship between different variables, which describe the state ofthe vehicle, is utilized in an elegant and, simultaneously, reliablemanner, namely, the relationship between, on one hand, the instantaneousspeed and the instantaneous yaw rate of the vehicle, which are to bedetermined, and the measurable values of the circumferential wheelspeed.

This may be accomplished, in particular, in that during and for thedetermination of the instantaneous speed and the instantaneous yaw rateof the vehicle, a Moore pseudoinverse of a transformation matrix betweena state of the base vehicle and a vector formed by the individual,ascertained circumferential wheel speeds is generated and applied to thevector formed by the individual, ascertained circumferential wheelspeeds, in order to provide the instantaneous speed and theinstantaneous yaw rate of the vehicle. In this context, in particular,the state of the vehicle describes the instantaneous speed and theinstantaneous yaw rate of the vehicle. Optionally, the path lengthtraveled by a wheel contact point, which may also be referred to asinstantaneous path length traveled by a wheel contact point, may also betaken into account for one or more wheels of the vehicle.

An advantage of the Moore pseudoinverse is its analytically specifiablerepresentation and structure, as well as its property of being able toinherently minimize or optimize a basic norm without numerical methodsor iteration.

A particularly high degree of accuracy in self-locating may be attained,if, in accordance with another advantageous further refinement of thedriving assistance method of the present invention, in addition to thecircumferential wheel speed, an instantaneous distance traveled by thecontact point of one or more wheels of the vehicle is measured,evaluated and taken as a basis for the determination of theinstantaneous speed, the instantaneous yaw rate, an instantaneousposition, and/or an instantaneous orientation of the vehicle.

In this context, a specific, instantaneous distance traveled by arespective contact point of a wheel of the vehicle may be measured andmade available via a respective wheel impulse counter, in view of asupplied value of the circumference of the wheel. Thus, due to thismeasure, measured values already supplied in an ESP system may be usedby the present invention.

In this context, the accuracy may increase further, if, in accordancewith another advantageous embodiment of the driving assistance method ofthe present invention, a specific, measured, instantaneouscircumferential wheel speed of one or more wheels of the vehicle and aspecific, measured, instantaneous distance traveled by the contact pointof one or more wheels of the vehicle are supplied to a Bayes filter and,in particular, to an extended Kalman filter, for evaluation, in order todetermine and/or check an instantaneous position and/or instantaneousorientation of the vehicle for plausibility.

According to a further aspect of the present invention, a control unitfor a driving assistance system of a vehicle is provided; the controlunit being configured to initiate, execute, control and/or regulate adriving assistance method of the present invention.

In addition, the subject matter of the present invention also includes adriving assistance system for a vehicle, as such; the driving assistancesystem being configured to initiate, execute, control and/or regulate adriving assistance method of the present invention; and/or the drivingassistance system including a control unit configured according to thepresent invention or having an operative connection to such a controlunit configured according to the present invention.

The driving assistance method of the present invention and the drivingassistance system of the present invention may be understood andimplemented purely by hardware, e.g., as a device for controlling theoperation of a vehicle, as well.

For example, an implementation as an ASIC is possible. As an alternativeto that, a purely process-engineering implementation, for example, inconnection with a computer implementation of the driving assistancemethod and driving assistance system of the present invention, isconceivable, preferably, in connection with, or as, a method forcontrolling the operation of a vehicle. Combined or mixed systems, inwhich partial aspects of the present invention are implemented byhardware and/or by software or process engineering, are alsoconceivable.

In addition, the present invention also provides a vehicle, as such. Thevehicle of the present invention is configured to be used by a drivingassistance method developed in accordance with the present invention.Alternatively, or in addition, the proposed vehicle is configured with adriving assistance system according to the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Specific embodiments of the present invention are described in detailwith reference to the figures.

FIG. 1 shows, in the form of a schematic block diagram, a vehicle, whichis configured according to the present invention, and in which aspecific embodiment of the driving assistance method of the presentinvention is used.

FIG. 2 shows a flow chart of a specific embodiment of a drivingassistance system according to the present invention, in the form of adriving assistance method.

FIG. 3 explains, in a schematic manner, different parameters used in aspecific embodiment of the driving assistance system or drivingassistance method of the present invention, with regard to the state ofa base vehicle.

FIGS. 4 through 7 show graphs for explaining the mode of operation ofspecific embodiments of the driving assistance system and drivingassistance method of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

Below, exemplary embodiments of the present invention and the technicalbackground are described in detail with reference to FIGS. 1 through 7.Identical and equivalent elements and components, as well as elementsand components functioning in the same or in an equivalent manner, aredenoted by the same reference numerals. The detailed description of thedenoted elements and components is not repeated in each case of theirappearance.

The depicted features and further characteristics may be isolated fromeach other and combined with each other as desired, without departingfrom the essence of the present invention.

FIG. 1 shows, in the form of a schematic block diagram, a vehicle 1,which is configured according to the present invention and utilizes aspecific embodiment of the driving assistance system 100 of the presentinvention and/or a specific embodiment of the driving assistance methodT according to the present invention.

The vehicle 1 according to the present invention is shown schematically,including a body 2, wheels 4, a drive unit 30 having a drive train 31,and a system 40 for steering and braking that possesses a steeringand/or brake train 41.

In addition, a control unit 50 for the underlying driving assistancesystem 100 of the present invention is provided; for example, thecontrol unit also being able to take the form of a part of a vehicle orengine control unit and setting up a connection to drive unit 30 andsystem 40 for braking and steering, via a control and/or acquisitionline 51.

Via control and/or acquisition line 51, control unit 50 is alsoconnected to sensors 10, namely, a first sensor 10-1 in the form of asensor for the circumferential wheel speed and a second sensor 10-2 inthe form of a wheel impulse counter.

During operation of vehicle 1, measuring signals with regard to thecircumferential wheel speed and/or with regard to the wheel speed orwith regard to the angle of rotation of the wheel, are supplied tocontrol unit 50 via corresponding sensors 10, 10-1, 10-2, and aresubjected to further processing and analysis, using a Bayes filter and,in particular, a Kalman filter 20, in order to generate and supply, onone hand, values for vehicle speed v and for yaw rate ω and, on theother hand, values of the distance traveled S by the specific contactpoint of a wheel 4, and to provide, from them, a position and/or anorientation of vehicle 1 in the surrounding area with a high degree ofreliability, even at low speeds of vehicle 1.

FIG. 2 shows a flow chart of a specific embodiment of a drivingassistance system 100 according to the present invention, taking theform of a driving assistance method T.

According to the essence, the specific embodiment of driving assistancemethod T of the present invention shown in FIG. 2 is subdivided into (i)a step T1 for ascertaining speed v and yaw rate ω of a vehicle 1; (ii) astep T2 of self-locating of vehicle 1 on the basis of supplied measuredvalues and/or data derived from them; (iii) a step T3 of monitoring andevaluating the surrounding area of the vehicle; as well as (iv) a stepT4 of controlling a vehicle unit on the basis of the self-locating andthe evaluation of the surrounding area of the vehicle.

Step T1 of ascertaining speed v and yaw rate ω of vehicle 1 issubdivided into a series of substeps T1-1 to T1-3.

In first substep T1-1, circumferential wheel speed V is acquired withregard to one or more wheels 4, in particular, through directmeasurement by a corresponding sensor 10-1 for the circumferential wheelspeed V of an associated wheel 4.

In second substep T1-2, a time delay possibly occurring during theacquisition of circumferential wheel speed V is compensated for, forexample, by temporal extrapolation into the future with the aid ofintegration with respect to time, as is explained below in detail inconnection with a preferred specific embodiment of the presentinvention.

Finally, in third substep T1-3, speed v and yaw rate ω of base vehicle 1are generated and made available.

In one specific embodiment of the present invention, step T2 of theself-locating of vehicle 1 may also be subdivided into a series ofsubsteps T2-1 to T2-3.

In a first substep T2-1, instantaneous distance traveled S by a wheelcontact point is acquired for one or more wheels 4, in particular,through direct measurement and/or in connection with measurement dataread out from a WIC sensor 10-2, based on a wheel radius, wheel diameterand/or wheel circumference of a respective, associated wheel 4 ofvehicle 1.

In a second substep T2-2, a Bayes filter and, in particular, a Kalmanfilter 20 are applied to the acquired data, namely, on one hand, tospeed v and yaw rate ω of base vehicle 1, and, on the other hand, to theacquired data regarding the instantaneous distances traveled S by thewheel contact points.

From this, the position and/or orientation of base vehicle 1 in itsenvironment is determined and/or checked for plausibility in a furthersubstep T2-3.

The data regarding position and/or orientation of vehicle 1 in itssurrounding area, which are generated in this manner with a high degreeof reliability, are then taken as a basis for the evaluation of thevehicle surroundings in step T3 and, as a result, for the control of atleast one vehicle unit in step T4, for example, in connection with thecontrol of a system 40 made up of steering and brakes and/or of a driveunit 30 of vehicle 1.

These and additional features and characteristics of the presentinvention are elucidated further with the aid of the followingexplanations:

Precise Self-Locating of a Vehicle

Increased customer acceptance of automated parking systems leads toincreasing usage of such systems. In this context, the performance ofthe overall system is evaluated by the user, and the concept ofself-locating is highly important in this connection.

In the context of the automated parking, two crucial and measurableaspects are (i) the presence or absence of curbs; and (ii) the minimumsize of a parking space required for a given vehicle. The influence ofthese aspects may be reduced, in order to improve the experience for thecustomer. However, more accurate locating of the vehicle during parkingis an important condition for achieving such an object.

The present invention provides a new method for using information, whichis derivable from ordinary ESP systems.

The action of the present invention increases the performance inautomated driving and parking systems, without requiring new oradditional sensors, and without the necessity of having to evaluate newand/or additional signals of ESP systems. In the case of low speeds,conventional self-locating algorithms utilize data, which may be readout of wheel impulse counters (WIC) used in the ESP system. Thecorresponding measured values are actually available at a known, fixedtime delay, but for evaluating the vehicle speed and the yaw rate, theyare acted upon by a comparatively high error due to quantization and aretherefore inaccurate and consequently do not allow for preciseself-locating in a vehicular application, such as in automated drivingor parking.

The more accurate measured values from sensors for the circumferentialwheel speeds or wheel rotational speeds (path length per unit time) arenot normally used.

This may be attributed to the fact that

-   (A) the measured values of the sensors for the circumferential wheel    speed or wheel rotational speed are not immediately available below    a particular threshold value of the acquisition time; and-   (B) the measured values of the sensors for the circumferential wheel    speed or wheel rotational speed are only available at a variable    delay. Consequently, the two are based on interrelated instances of    signal preprocessing and corresponding time-out conditions.

Estimation of the Vehicle speed and Yaw Rate

In the following, it is described how accurate estimations of thevehicle speed and of the yaw rate of base vehicle 1 are generated fromthe four available circumferential wheel speeds V=(V^(FrL) V^(FrR)V^(RrL) V^(RrR))^(T)ϵ

⁴ or wheel rotational speeds.

According to the present invention, vehicle 1 may have, in general, afour-wheel steering system. This means that according to the presentinvention, all four wheels 4 of vehicle 1 may be steered.

In addition, in the method of the present invention and in theimplementation as an algorithm, real-time implementation may beachieved, although in one embodiment of the method according to thepresent invention, a matrix inversion is included in the evaluation.

For example, through use of an extended information filter, thedimension of the matrix to be inverted may be reduced so much incomparison with an extended Kalman filter, that the method of thepresent invention and the algorithm remain real-time capable because oflow computing time.

In addition, in other embodiments of the method according to the presentinvention, delay compensation may be initiated, so that, in particular,measured values from sensors for circumferential wheel speed or wheelrotational speed may be used.

Speed and Yaw Rate of a Vehicle from the Wheel Speeds

If yaw rate ω, that is, the change in the yaw angle of vehicle 1 overtime, and the speed v of vehicle 1 are given and are represented as astate x=(v ω)^(T)ϵ

², then, with the aid of a suitable transformation matrix H(u)ϵ

^(4×2), wheel rotational speeds V, which are also referred to as wheelspeeds or circumferential wheel speeds (all of the terms are usedsynonymously), may be represented by the following expression:

V=H(u)·x  (1.1.1)

H(u)=(cos(δ−γ)r ^(x)·sin δ−r ^(y)·cos δ)  (1.1.2)

u=(δγr ^(x) r ^(y))^(T)  (1.1.3)

Only values of measurements of the circumferential wheel speeds or wheelspeeds V are given, but not state x, as such.

Therefore, it is desirable to find the best estimate of state x, whichminimizes the value of an underlying norm selected as a measure ofquality, thus, in this case, e.g., the minimum norm:

min∥V−H(u)·{circumflex over (x)}∥  (1.1.4)

This problem may be solved by determining and utilizing thepseudoinverse pinv(H(u)) associated with the matrix H(u) (instead of theinverse actually required). This is either the unique least squaressolution, or it is the least squares solution of the minimum normaccording to 1.1.4:

{circumflex over (x)}=pinv(H(u))·V  (1.1.5)

Analytical Solution of the Pseudoinverse

The elegance of the use of the pseudoinverse pinv(H(u)) according to thepresent invention is that the pseudoinverse pinv(H(u)) of the matrixH(u) may be calculated analytically, which means that the computationalmethod may be implemented easily in a real-time application, forexample, on the basis of the following expressions 1.1.6:

$\begin{matrix}{{H = {\begin{pmatrix}a & c & e & g \\b & d & f & h\end{pmatrix}^{T} \in {\mathbb{R}}^{4 \times 2}}}{{{pinv}(H)} = {\frac{1}{j}\begin{pmatrix}{{d^{2}a} + {f^{2}a} + {h^{2}a} - {dbc} - {fbe} - {hbg}} & {{- {cad}} - {eaf} - {gah} + {c^{2}b} + {e^{2}b} + {g^{2}b}} \\{{b^{2}c} + {f^{2}c} + {h^{2}c} - {bad} - {fde} - {hdg}} & {{- {abc}} - {efc} - {ghc} + {a^{2}d} + {e^{2}d} + {g^{2}d}} \\{{b^{2}e} + {d^{2}e} + {h^{2}e} - {baf} - {dcf} - {hfg}} & {{- {abe}} - {cde} - {ghe} + {a^{2}f} + {c^{2}f} + {g^{2}f}} \\{{d^{2}a} + {f^{2}a} + {h^{2}a} - {bah} - {dch} - {feh}} & {{- {abg}} - {cdg} - {efg} + {a^{2}h} + {c^{2}h} + {e^{2}h}}\end{pmatrix}^{T}}}{j = {{b\left( {{c\left( {{bc} - {ad}} \right)} - {afe} - {ahg} + {be}^{2} + {bg}^{2}} \right)} + {a\left( {{ad}^{2} + {af}^{2} + {ah}^{2} - {bcd} - {bef} - {bgh}} \right)} - {cfde} - {decf} - {chdg} - {dgch} + {c^{2}f^{2}} + {c^{2}h^{2}} + {d^{2}e^{2}} + {d^{2}g^{2}} - {fgeh} - {ehfg} + {e^{2}h^{2}} + {f^{2}g^{2}}}}} & \left( {1.1{.6}} \right)\end{matrix}$

Delay Compensation for Vehicle Speed and Yaw Rate

At a time K=k·Ts, a direct speed measurement having the value V_(k) isnot available due to the time delay of the signals. Assuming thatmeasurements V_(l) at time L=l·Ts with k>l, the corresponding states xmay be determined, for example, according to (1.1.7):

{circumflex over (x)} _(l) =pinv(H(u _(l)))·V _(l)  (1.1.7)

An option for determining values at the later time K=k·T_(s) may be, forexample, to integrate the changes in state x with respect to time, thatis, from time L to time K, for example, according to expression (1.1.8):

$\begin{matrix}{{\hat{x}(K)} = {{\hat{x}(L)} + {\int_{t = L}^{K}{\frac{d{\hat{x}(t)}}{dt}{dt}}}}} & \left( {1.1{.8}} \right)\end{matrix}$

The derivative {dot over (x)} of state x with respect to time may beascertained from acceleration measurements Aϵ

and a single-track model, which supplies the distance Rϵ

from the center of rotation. This yields the expression (1.1.9):

$\begin{matrix}{\frac{dx}{dt} = {\overset{.}{x} = {\begin{pmatrix}\overset{.}{\omega} \\\overset{.}{v}\end{pmatrix} = {\begin{pmatrix}{\frac{d}{dt}\left( \frac{v}{R} \right)} \\a\end{pmatrix} \approx \begin{pmatrix}\frac{\Lambda}{R} \\A\end{pmatrix}}}}} & \left( {1.1{.9}} \right)\end{matrix}$

Consequently, a representation of the state {circumflex over (x)} attime K results in accordance with expression (1.1.10):

$\begin{matrix}{{\hat{x}}_{k} = {\begin{pmatrix}{\hat{V}}_{k} \\{\hat{\Omega}}_{k}\end{pmatrix} = {{\hat{x}}_{l} + {\sum\limits_{j = l}^{k - 1}\; {\begin{pmatrix}\frac{A_{j}}{R_{j}} \\A_{j}\end{pmatrix} \cdot \frac{T_{s}}{k - l - 1}}}}}} & \left( {1.1{.10}} \right)\end{matrix}$

To calculate the values for such a representation according toexpression (1.1.10), measured values of acceleration A and of the centerof rotation, that is, of the corresponding distance R of the center ofrotation with regard to the single-track model, must be available andknown without significant delay. In the case of use of measurements froman ESP system with regard to the acceleration, an offset estimation mustbe implemented.

Application of the Concept of Measurement and Simulation

In FIGS. 4 and 5, traces 143-1 to 153-3 of different signals for the yawrate and speed as a function of time t, namely, as part of a scenario ofparallel parking, are represented in the form of graphs 140, 150.

Solid traces 143-1, 153-1 relate to a reference system, which isutilized for representing the actual conditions. The measurements inrelation to the reference system are recorded by an inertial measurementunit, which is coupled to a DGPS system, in order to compensate forsensor errors, such as offset, drift and gain.

The values calculated from the circumferential wheel speeds or wheelspeeds are represented as derived values or estimates, in the form ofdashed lines, in traces 143-2, 153-2. They have a time delay and aredetermined according to expression (1.1.7).

The measurements compensated for in the time delay by accelerationmeasurements are represented pointwise in traces 143-3, 153-3. Thecorresponding values are generated in accordance with expression(1.1.10).

In graphs 140 and 150 of FIGS. 4 and 5, the time is plotted on abscissas141 and 151. The yaw rate and the vehicle speed are plotted on ordinates142 and 152, respectively.

Merging Plan

Using a Bayes filter and, in particular, an extended Kalman filter,together with the above-described pseudoinverse for the actualtransformation matrix H(u), measurements of values of circumferentialwheel speed V and values of a distance traveled by wheel contact pointsor centers of tire contact S may be merged or connected to each other.

To that end, a system function ƒϵ

³ and a measuring function hϵ

⁹ are introduced. The system function describes how vehicle speed vϵ

, vehicle yaw rate ωϵ

and distances traveled sϵ

⁴ by the centers of tire contact develop with time. A representationaccording to expression (1.2.1) results:

$\begin{matrix}{x_{k + 1} = {\begin{pmatrix}v_{k + 1} \\\omega_{k + 1} \\s_{k + 1}\end{pmatrix} = {{f\left( {x_{k},u_{k}} \right)} = \begin{pmatrix}{v_{k} + {A_{k} \cdot T_{s}}} \\\omega_{k} \\{s_{k} + {\left\lbrack {{\left( {v_{k} + {a_{k} \cdot T_{s}}} \right) \cdot {\cos \left( {\delta_{k} - \gamma_{k}} \right)}} + {\omega_{k} \cdot \left( {{{r^{x} \cdot \sin}\mspace{14mu} \delta_{k}} - {{r^{y} \cdot \cos}\mspace{14mu} \delta_{k}}} \right)}} \right\rbrack \cdot T_{s}}}\end{pmatrix}}}} & \left( {1.2{.1}} \right)\end{matrix}$

In this representation, T_(s) is the sampling time. Variables r^(x) andr^(y) denote the contact point vectors. Variable δ denotes the vector ofthe individual wheel rotational angles. The component representations(1.2.2) for these variables are as follows:

s=(s ^(FrL) s ^(FrR) s ^(RrL) s ^(RrR))^(T)

r ^(x)=(r ^(x,FrL) r ^(x,FrR) r ^(x,RrL) r ^(x,RrR))^(T)

r ^(y)=(r ^(y,FrL) r ^(y,FrR) r ^(y,RrL) r ^(y,RrR))^(T)

δ=(δ^(FrL)δ^(FrR)δ^(RrL)δ^(RrR))^(T)  (1.2.2)

Measuring function h describes how the values of measurements z may bedetermined as a function of system states x and input values u. Thefollowing component representation (1.2.3) is yielded:

$\begin{matrix}{z_{k} = {\begin{pmatrix}{\hat{V}}_{k} \\{\hat{\Omega}}_{k} \\S_{k}\end{pmatrix} = {{h\left( {x_{k},u_{k}} \right)} = \begin{pmatrix}v_{k} \\\omega_{k} \\{s_{k} + {\left\lbrack {{\left( {v_{k} + {a_{k} \cdot T_{s}}} \right) \cdot {\cos \left( {\delta_{k} - \gamma_{k}} \right)}} + {\omega_{k} \cdot \left( {{{r^{x} \cdot \sin}\mspace{14mu} \delta_{k}} - {{r^{y} \cdot \cos}\mspace{14mu} \delta_{k}}} \right)}} \right\rbrack \cdot T_{s}}}\end{pmatrix}}}} & \left( {1.2{.3}} \right)\end{matrix}$

The following variables occur in this representation in accordance withcomponent representation (1.2.4):

S=(S ^(FrL) S ^(FrR) S ^(RrL) S ^(RrR))^(T)  (1.2.4)

In this context, variable S^(i) denotes the distance traveled by thecorresponding wheel contact point; the distance traveled being able tobe ascertained on the basis of the corresponding circumference ofassociated wheel 4 and the value read out of the WIC sensor. Variables{circumflex over (V)}_(k) and {circumflex over (Ω)}_(k) denote thevalues or estimates of values of the speed and the yaw rate,respectively, using the above-mentioned formulation.

{circumflex over (x)} _(k|k-1)=ƒ({circumflex over (x)} _(k-1|k-1))

prediction of the state: P _(k|k-1) =F _(k) ·P _(k-1|k-1) ·F+Q _(k)

{circumflex over (z)} _(k) =h({circumflex over (x)} _(k|k-1))

S _(k) =H _(k) ·P _(k|k-1) ·H _(k) ^(T) +R _(k)

prediction of the measurement: Ψ_(k) =P _(k|k-1) ·H _(k) ^(T)

{circumflex over (x)} _(k|k) ={circumflex over (x)} _(k|k-1) +K _(k)·(z_(k) −{circumflex over (z)} _(k))

P _(k|k) =P _(k|k-1) −K _(k) ·H _(k) ^(T) S _(k) ⁻¹  (1.2.5)

updating, using measurement: K _(k)=Ψ_(k) ·S _(k) ⁻¹

In the relations according to (1.2.5), P denotes the system covariance,S denotes the innovation covariance, K denotes the Kalman gain, Qdenotes the system noise, and R denotes the measuring noise. T denotesan auxiliary variable.

Matrices F and H are defined in relation to expressions (1.2.6) and(1.2.7).

In one preferred specific embodiment, a Bayes Filter and, in particular,an expanded Kalman filter are used in accordance with the above scheme(1.2.5), in order to determine or estimate the values of v and ω. Inthis context, the complete state, which includes S, is generallyascertained.

In this instance, however, S is integrated only from v and ω. In thismanner, the position of vehicle 1, which may be calculated from v and ω,may be ascertained outside of the filter. The representation accordingto expression (1.2.6) results for this:

$\begin{matrix}{\mspace{76mu} {{F = \frac{\partial f}{\partial x}}{H\overset{def}{=}\begin{pmatrix}1 & 0 & 0 & 0 & 0^{1 \times 4} \\0 & 1 & 0 & 0 & 0^{1 \times 4} \\0^{4 \times 1} & 0^{4 \times 1} & {T_{s} \cdot {\cos \left( {\delta - \gamma} \right)}} & {T_{s} \cdot \left( {{{r^{x} \cdot \sin}\mspace{14mu} \delta} - {{r^{y} \cdot \cos}\mspace{14mu} \delta}} \right)} & 0^{4 \times 4}\end{pmatrix}}}} & \left( {1.2{.6}} \right)\end{matrix}$

In this context, it should be noted that

${H \neq \frac{\partial h}{\partial x}},$

since the lower right (4×4) submatrix of H is not an identity matrix.The following is yielded:

$\begin{matrix}{\frac{\partial h}{\partial x} = \begin{pmatrix}1 & 0 & 0 & 0 & 0^{1 \times 4} \\0 & 1 & 0 & 0 & 0^{1 \times 4} \\0^{4 \times 1} & 0^{4 \times 1} & {T_{s} \cdot {\cos \left( {\delta - \gamma} \right)}} & {T_{s} \cdot \left( {{{r^{x} \cdot \sin}\mspace{14mu} \delta} - {{r^{y} \cdot \cos}\mspace{14mu} \delta}} \right)} & 1^{4 \times 4}\end{pmatrix}} & \left( {1.2{.7}} \right)\end{matrix}$

In this instance, s may not be influenced directly by a measurement ofS. Nevertheless, s is corrected indirectly via the states or values of vand ω.

In this manner, the position of vehicle 1 may be determined orestimated, namely, from the states or values of v and ω, and via thedistance traveled, namely, in accordance with and in agreement with thepath of the contact points.

Simulation Results

In FIGS. 6 and 7, simulation results for the same sequence as describedabove are represented in graphs 160 and 170.

In graphs 160 and 170 of FIGS. 6 and 7, the time is plotted on abscissas161 and 171. The yaw rate and the vehicle speed are plotted on ordinates162 and 172, respectively.

Solid traces 163-1 and 173-1 relate again to reference measurements, thetraces 163-2 and 173-2 represented as dashed lines relate to values,which are generated, using a Bayes Filter and, in particular, anextended Kalman filter 20 (EKF).

It is apparent that, in particular, during the time in which apseudo-measurement of speed v and yaw rate ω is available, the finaldetermination or estimate utilizing the Bayes filter and, in particular,the extended Kalman filter 20, is highly effective. The accuracy of theangular rate may be improved further through pseudo-measurements, usinga single-track model, or simply by measurements of the yaw rate.

1-10. (canceled)
 11. A driving assistance method for a vehicle,comprising the following steps: ascertaining an instantaneous speed ofthe vehicle and an instantaneous yaw rate of the vehicle; and carryingout an operation of self-locating of the vehicle based on theascertained instantaneous speed of the vehicle and the ascertainedinstantaneous yaw rate of the vehicle; wherein an instantaneouscircumferential wheel speed of one or more wheels of the vehicle isdirectly measured, evaluated and used as a basis for the ascertaining ofthe instantaneous speed of the vehicle and the instantaneous yaw rate ofthe vehicle.
 12. The driving assistance method as recited in claim 11,wherein a specific, instantaneous circumferential wheel speed ismeasured and made available by a circumferential wheel speed sensor. 13.The driving assistance method as recited in claim 11, wherein a timedelay of the measured instantaneous circumferential wheel speed iscompensated for by temporally extrapolating measured values at anearlier measuring time to a current evaluation time, by integrating withrespect to time, from the earlier measuring time to the currentevaluation time, based on one or more measured values of aninstantaneous acceleration of the vehicle and/or based on a single-trackmodel of the vehicle.
 14. The driving assistance method as recited inclaim 11, wherein during the ascertaining of the instantaneous speed ofthe vehicle and the instantaneous yaw rate of the vehicle, an operationof Moore pseudoinversion is provided and applied to the ascertainedcircumferential wheel speed.
 15. The driving assistance method asrecited in claim 11, wherein during and for the ascertaining of theinstantaneous speed of the vehicle and the instantaneous yaw rate of thevehicle, a Moore pseudoinverse of a transformation matrix between astate of the vehicle and a vector formed by the individual, ascertainedcircumferential wheel speeds is generated and applied to the vectorformed by the individual, ascertained circumferential wheel speeds, inorder to provide the instantaneous speed of the vehicle and theinstantaneous yaw rate of the vehicle.
 16. The driving assistance methodas recited in claim 11, wherein: an instantaneous distance traveled by acontact point of one or more wheels of the vehicle is measured,evaluated and used as a basis for the ascertaining of the instantaneousspeed of the vehicle, and/or the instantaneous yaw rate of the vehicle,and/or an instantaneous position of the vehicle, and/or an instantaneousorientation of the vehicle; and a specific, instantaneous distancetraveled by a respective contact point of a wheel of the vehicle ismeasured and made available via a respective wheel impulse counter inview of a supplied value of a circumference of the wheel.
 17. Thedriving assistance method as recited in claim 16, wherein a specific,measured instantaneous circumferential wheel speed of one or more wheelsof the vehicle and a specific, measured, instantaneous distance traveledby the contact point of one or more wheels of the vehicle are suppliedto a Bayes filter and an extended Kalman filter for evaluation, and/orfor plausibility-checking, and/or for determining an instantaneousposition and/or instantaneous orientation of the vehicle.
 18. A controlunit for a driving assistance system of a vehicle, the control unitconfigured to: ascertain an instantaneous speed of the vehicle and aninstantaneous yaw rate of the vehicle; and carry out an operation ofself-locating of the vehicle based on the ascertained instantaneousspeed of the vehicle and the ascertained instantaneous yaw rate of thevehicle; wherein an instantaneous circumferential wheel speed of one ormore wheels of the vehicle is directly measured, evaluated and used as abasis for the ascertaining of the instantaneous speed of the vehicle andthe instantaneous yaw rate of the vehicle.
 19. A driving assistancesystem for a vehicle, comprising: a control unit configured to:ascertain an instantaneous speed of the vehicle and an instantaneous yawrate of the vehicle; and carry out an operation of self-locating of thevehicle based on the ascertained instantaneous speed of the vehicle andthe ascertained instantaneous yaw rate of the vehicle; wherein aninstantaneous circumferential wheel speed of one or more wheels of thevehicle is directly measured, evaluated and used as a basis for theascertaining of the instantaneous speed of the vehicle and theinstantaneous yaw rate of the vehicle.
 20. A vehicle, comprising: adriving assistance system for a vehicle, comprising: a control unitconfigured to: ascertain an instantaneous speed of the vehicle and aninstantaneous yaw rate of the vehicle; and carry out an operation ofself-locating of the vehicle based on the ascertained instantaneousspeed of the vehicle and the ascertained instantaneous yaw rate of thevehicle; wherein an instantaneous circumferential wheel speed of one ormore wheels of the vehicle is directly measured, evaluated and used as abasis for the ascertaining of the instantaneous speed of the vehicle andthe instantaneous yaw rate of the vehicle.